Good question! If look closely at the mouths of Predators, you'll notice that although they are frightening, they don't seem well designed for, well, eating food. How does a Predator masticate? Wolf Gnards studied the arrangement and apparent functions of all ten of an adult Predator's teeth and posed two hypotheses: either a Predator grinds food into a fine paste, like baby food, or swallows its food whole, like a snake. I'm inclined to support the Paste Theory:
Like Robocop, the Predators subsist off a "rudimentary paste that sustains their organic systems." The fact that Robocop eats baby food is pretty good evidence that a big, strong killing machine can thrive off the stuff. Baby food is probably also convenient for space travel like astronaut ice cream or Tang, or like military MRE’s (which are a little more like dog food, but I think a Predator might enjoy that more though). I do have a hard time believing that the Predator race has the manufacturing infrastructure and know-how to market and mass produce Brand X Predator baby mush (with the meaty gravy that babies craze). However, this same sentiment could also be suggested for spaceships/space travel. I like to imagine that faster than light travel requires more book reading and less laser shooting. Most likely if they do eat some sort of gruel it is composed of the bones of their fallen prey; any meat grinder would do in that case.
The biggest teeth reminded me of a crab. Their function is to pull in food, and then I figured the food (anything, really) was broken down by a highly acidic digestive system.
As for the Predator's sluggish movements... what sort of atmosphere did it come from? I live in Colorado. It's interesting to watch the tourists at Rocky Mountain National Park, who are visiting from sea level. They get dried out, develop headaches, fatigue easily just walking around in the thinner atmosphere. It takes awhile to acclimate here. How much harder would it be for a being from a different planet? What were the natural upper limits to the Predator's capacity for adaptation, unaided by technology?
They look to be useful for capturing a prey animal that is hiding in a burrow - just stick your head in and use your prehensile tusks to grab your meal. Later, when the Predator evolved from quadruped to biped, the tusks were repurposed to new functions. Now that the Predator is a biped, the most obvious function for these mobile tusks is communication, much like we use our facial muscles and display our bony teeth. Originally, when hominids displayed teeth, it was a warning or an aggressive act -- now we are simply smiling. Hominids also used their teeth for fighting, now, we usually don't do this, at least after the age of 24 or 25.
So....my theory is that the mobile tusks are used in the way humans use their facial muscles -- for communication (and the films seem to support this.) I am willing to bet the predictor species are not only warriors - the warrior caste is the only one we have encountered.
I bet there are Predators who fret and worry to the point of going to a plastic surgeon to make their tusks more appealing, more sexy. Especially Predators trying to make it big in entertainment, or marry that certain sugar-daddy or sugar-momma.